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    "# Options Handler Tutorial\n",
    "Varying options with time is a well regarded technique in particle swarm optimization for faster convergence and\n",
    "better solutions. This class exposes methods to do the same.\n",
    "\n",
    "In this example, we will demonstrate some common variation techniques along with some [visualisation].\n",
    "- `oh_strategy`: a dictionary containing the strategies for each option\n",
    "- `end_opts`: a dictionary containing the ending options for each option\n",
    "- `plot_cost_history`: for plotting the cost history of a swarm given a matrix\n",
    "- `plot_contour`: for plotting swarm trajectories of a 2D-swarm in two-dimensional space\n",
    "\n",
    "[visualisation]: https://github.com/ljvmiranda921/pyswarms/blob/master/docs/examples/tutorials/visualization.ipynb\n"
   ],
   "cell_type": "markdown",
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    "collapsed": true,
    "pycharm": {
     "name": "#%% md\n"
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   }
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   "outputs": [],
   "source": [
    "# Import modules\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from IPython.display import Image\n",
    "\n",
    "# Import PySwarms\n",
    "import pyswarms as ps\n",
    "from pyswarms.utils.functions import single_obj as fx\n",
    "from pyswarms.utils.plotters import (plot_cost_history, plot_contour)\n",
    "\n",
    "from pyswarms.backend.handlers import OptionsHandler"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "source": [
    "Let's create some optimizers for comparison. Here, we're going to use Global-best PSO to find the minima\n",
    "of a sphere function. As usual, we simply create an instance of its class `pyswarms.single.GlobalBestPSO`\n",
    "by passing the required parameters that we will use. Then, we'll call the `optimize()` method for 100 iterations for both and visualise the results"
   ],
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   }
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  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "2020-12-11 19:23:18,434 - pyswarms.single.global_best - INFO - Optimize for 100 iters with {'c1': 0.5, 'c2': 0.3, 'w': 0.9}\n",
      "pyswarms.single.global_best: 100%|██████████|100/100, best_cost=7.95e-10\n",
      "2020-12-11 19:23:18,540 - pyswarms.single.global_best - INFO - Optimization finished | best cost: 7.946552028624106e-10, best pos: [ 2.74938126e-05 -6.22458616e-06]\n",
      "2020-12-11 19:23:18,541 - pyswarms.single.global_best - INFO - Optimize for 100 iters with {'c1': 0.5, 'c2': 0.3, 'w': 0.9}\n",
      "pyswarms.single.global_best: 100%|██████████|100/100, best_cost=7.99e-28\n",
      "2020-12-11 19:23:18,648 - pyswarms.single.global_best - INFO - Optimization finished | best cost: 7.987498732542365e-28, best pos: [ 7.14102116e-15 -2.73451219e-14]\n"
     ]
    }
   ],
   "source": [
    "options = {'c1':0.5, 'c2':0.3, 'w':0.9}  # starting options\n",
    "optimizer_without_handle=ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=options)\n",
    "optimizer_with_handle = ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=options, oh_strategy={\"w\":'exp_decay', 'c1':'lin_variation'})\n",
    "\n",
    "cost, pos = optimizer_without_handle.optimize(fx.sphere, iters=100)\n",
    "cost_h, pos_h = optimizer_with_handle.optimize(fx.sphere, iters=100)\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Comparing the cost history\n",
    "\n",
    "To plot the cost history, we simply obtain the `cost_history` from the `optimizer` class and pass it to the `cost_history` function. In addition, we can obtain the following histories from the same class:\n",
    "- mean_neighbor_history: average local best history of all neighbors throughout optimization\n",
    "- mean_pbest_history: average personal best of the particles throughout optimization"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
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6SpIkSdI4Z/CTJEmSpHHO4CdJkiRJ49y4meMnSRPNxo0bWb16NRs2bGi6KV0zffp05syZw5QpU5puiiRpO2H/WM3gJ0nbqdWrV7Pzzjszd+5cIqLp5tQuM1m3bh2rV69m3rx5TTdHkrSdsH+sZqmnJG2nNmzYwMyZM8dlpwYQEcycOXNcf2MrSaqf/WM1g58kbcfGa6c2ZLw/P0lSd4z3/mNbnp/BT5IkSZLGOYOfJGmb3X///Rx77LE897nPZf/99+dP/uRP+OEPf7hVx/joRz/apdZJktScfusjDX6SpG2SmbzmNa/h0EMP5cc//jE33XQTH/vYx3jggQe26jgGP0nSeNOPfaTBT5K0Ta6++mqmTJnCW9/61qeWvfCFL+Sggw7i/e9/P/vssw+/93u/x+WXXw7AmjVrOOSQQ9h3333ZZ599uO666zj55JP59a9/zb777svrXve6pp6KJEm16sc+0j/nIEnjQLcmsWdmx3Xf//732X///bdY/uUvf5lbb72V7373u/ziF7/ggAMO4JBDDuFf/uVfeOUrX8mpp57Kpk2beOyxxzj44IM599xzufXWW7vSfknSxNZE/wj92Uca/CRJtfrWt77Fcccdx8DAALvtthsve9nLuPHGGznggAN485vfzMaNGznyyCPZd999m26qJEk91WQfaamnJI0DmdmVn+Hsvffe3HTTTaNu4yGHHMK1117L7NmzeeMb38jnP//5sT5tSZKG1UT/CP3ZRzriV7r99ttZtmzZNu07ffp0jjrqKHbZZZd6GyVJfewVr3gFH/zgB1myZAmLFy8G4Hvf+x677LILl19+OccffzwPPvgg1157LZ/4xCf4yU9+wpw5c3jLW97C448/zs0338wb3vAGpkyZwsaNG5kyZUrDz0idXHrppTz00EPbtO+CBQt4xSteUXOLJKm/9WMfafAr3XDDDbzjHe/Y5v1//OMf87GPfazGFklSf4sIvvKVr/Dud7+bs846i+nTpzN37lzOOeccHn30UV74whcSEfz93/89v/3bv83FF1/MJz7xCaZMmcJOO+301LeZixcv5gUveAH77bcfl156acPPSlXOPPNM7rjjjm3ad9KkSaxZs4ZnPvOZNbdKkvpXP/aRMZqhyu3BwoULc8WKFdu8//XXX79NJ3PlypVcc801vOUtb2HJkiXb/PiStLXuuOMO9tprr6ab0XVVzzMibsrMhQ01absz1j7yIx/5CPfff/9W7/fP//zPrF+/njvvvJPnPe952/z4krQ17B+r+0dH/EovfelLeelLX7rV+51//vlcc801bNq0qQutkiSpeR/60Ie2ab9ly5axfv16BgcHa26RJGlreXGXMZo0qTiFBj9JkjY3eXLx/bLBT5KaZ/Abo4GBAQCefPLJhlsiaSIaL+X6nYz35zfeDfWRfjkqqdfGe/+xLc/P4DdGdmqSmjJ9+nTWrVs3bju3zGTdunVMnz696aZoGzniJ6kJ9o/VnOM3RpZ6SmrKnDlzWL16NWvXrm26KV0zffp05syZ03QztI0MfpKaYP9YzeA3RpZ6SmrKlClTmDdvXtPNkDoy+Elqgv1jNUs9x8hST0mSqtlHSlL/6Grwi4jDI+LOiFgVESdXrJ8WEZeX65dHxNy29XtExKMRcVI32zkWlnpKklTNET9J6h9dC34RMQCcBxwBLACOi4gFbZudADyUmXsCZwNnta3/FPDv3WpjHSz1lCSpmsFPkvpHN0f8DgRWZeZdmfkEcBmwqG2bRcDF5e0rgMMiIgAi4kjgbmBlF9s4ZpaxSJJUzeAnSf2jm8FvNnBvy/3V5bLKbTJzEFgPzIyInYAPAH833ANExOKIWBERK5q6ao+lnpIkVfPLUUnqH/16cZcPA2dn5qPDbZSZSzJzYWYunDVrVm9a1sZST0mSqjniJ0n9o5t/zuE+YPeW+3PKZVXbrI6IycAMYB3wYuCoiPh7YBfgyYjYkJnndrG928RvMyVJqmbwk6T+0c3gdyMwPyLmUQS8Y4G/aNtmKXA8cD1wFLAsMxM4eGiDiPgw8Gg/hj6w1FOSpE4MfpLUP7oW/DJzMCJOBK4CBoALM3NlRJwBrMjMpcAFwCURsQp4kCIcblcc8ZMkqZp9pCT1j26O+JGZVwJXti07veX2BuDoEY7x4a40ribO8ZMkqZojfpLUP/r14i7bDb/NlCSpmsFPkvqHwW+MnOMnSVI1g58k9Q+D3xhZ6ilJUjWrYiSpfxj8xshOTZKkao74SVL/MPiNkaWekiRVM/hJUv8w+I2RpZ6SJFUz+ElS/zD4jZGlnpIkVRvqIw1+ktQ8g98YWeopSVK1oRE/+0hJap7Bb4ws9ZQkqZqlnpLUPwx+Y2SppyRJ1Qx+ktQ/DH5jZKmnJEnVnOMnSf3D4DdGlnpKkjqJiMMj4s6IWBURJ1esnxYRl5frl0fE3HL5zIi4OiIejYhzW7Z/WkT8W0T8ICJWRsTHe/h0tppz/CSpfxj8xshST0lSlYgYAM4DjgAWAMdFxIK2zU4AHsrMPYGzgbPK5RuA04CTKg79ycx8PvAi4A8i4ohutL8OlnpKUv8w+I2RpZ6SpA4OBFZl5l2Z+QRwGbCobZtFwMXl7SuAwyIiMvNXmfktigD4lMx8LDOvLm8/AdwMzOnmkxgLg58k9Q+D3xhZ6ilJ6mA2cG/L/dXlssptMnMQWA/MHM3BI2IX4NXANzqsXxwRKyJixdq1a7eu5TVxjp8k9Q+D3xhZ6ilJ6rWImAx8AfhMZt5VtU1mLsnMhZm5cNasWb1tYMk5fpLUPwx+Y2SppySpg/uA3VvuzymXVW5ThrkZwLpRHHsJ8KPMPGfszeweSz0lqX8Y/MbIUk9JUgc3AvMjYl5ETAWOBZa2bbMUOL68fRSwLDNzuINGxEcoAuK7621u/Qx+ktQ/JjfdgO2dpZ6SpCqZORgRJwJXAQPAhZm5MiLOAFZk5lLgAuCSiFgFPEgRDgGIiHuApwNTI+JI4I+BXwKnAj8Abo4IgHMz8/yePbGt4Bw/SeofBr8xstRTktRJZl4JXNm27PSW2xuAozvsO7fDYaOu9nWbc/wkqX9Y6jlGlnpKklTNUk9J6h8GvzFqDX4jTMuQJGlCMfhJUv8w+I1RRFDOsXDUT5KkFs7xk6T+YfCrwdA8P4OfJEm/4Rw/SeofBr8aeGVPSZK2ZKmnJPUPg18NDH6SJG3J4CdJ/cPgVwP/pIMkSVtyjp8k9Q+DXw38kw6SJG3JOX6S1D8MfjWw1FOSpC1Z6ilJ/cPgVwNLPSVJ2pLBT5L6h8GvBpZ6SpK0JYOfJPUPg18NLPWUJGlL9o+S1D8MfjWw1FOSpC054idJ/cPgVwNLPSVJ2pLBT5L6h8GvBpaySJK0JYOfJPUPg18NLPWUJGlLfjEqSf3D4FcDSz0lSdqSI36S1D8MfjXwG01JkrZk8JOk/mHwq4GlnpIkbcngJ0n9w+BXA0s9JUnakhUxktQ/DH41sGOTJGlLjvhJUv8w+NXAUk9JkrbU+sVoZjbcGkma2Ax+NbDUU5KkLUWEVTGS1CcMfjWwU5MkqZp9pCT1B4NfDezUJEmq5jw/SeoPBr8aDM3xs9RTkqTNGfwkqT8Y/GrgiJ8kSdUMfpLUHwx+NTD4SZJUzT5SkvqDwa8GlnpKklTNET9J6g8Gvxr4baYkSdUMfpLUHwx+NTD4SZJUzeAnSf3B4FcDSz0lSao29OWowU+SmmXwq4EjfpIkVRsa8bOPlKRmGfxqYPCTJKmapZ6S1B8MfjUYKvU0+EmStDmDnyT1B4NfDYZG/JzjJ0nS5pzjJ0n9weBXA0s9JUmq5hw/SeoPBr8aWOopSVI1Sz0lqT8Y/GpgqackSdUMfpLUHwx+NbDUU5Kkas7xk6T+YPCrgaWekiRVc46fJPUHg18NLPWUJKmapZ6S1B8MfjWw1FOSpGoGP0nqDwa/GljqKUmqEhGHR8SdEbEqIk6uWD8tIi4v1y+PiLnl8pkRcXVEPBoR57bts39E3Fbu85mIiB49nW3iHD9J6g8GvxpY6ilJahcRA8B5wBHAAuC4iFjQttkJwEOZuSdwNnBWuXwDcBpwUsWhPwu8BZhf/hxef+vr4xw/SeoPBr8aWOopSapwILAqM+/KzCeAy4BFbdssAi4ub18BHBYRkZm/ysxvUQTAp0TEs4CnZ+YNmZnA54Eju/kkxspST0nqDwa/Ghj8JEkVZgP3ttxfXS6r3CYzB4H1wMwRjrl6hGMCEBGLI2JFRKxYu3btVja9PgY/SeoPBr8aDM3xs9RTktQvMnNJZi7MzIWzZs1qrB3O8ZOk/mDwq4EjfpKkCvcBu7fcn1Muq9wmIiYDM4B1IxxzzgjH7CvO8ZOk/mDwq4HBT5JU4UZgfkTMi4ipwLHA0rZtlgLHl7ePApaVc/cqZeYa4JcR8ZLyap5vAP61/qbXx1JPSeoPk5tuwHhgqackqV1mDkbEicBVwABwYWaujIgzgBWZuRS4ALgkIlYBD1KEQwAi4h7g6cDUiDgS+OPMvB14G3ARsAPw7+VP3zL4SVJ/MPjVwBE/SVKVzLwSuLJt2ekttzcAR3fYd26H5SuAfeprZXc5x0+S+oOlnjUw+EmSVM05fpLUHwx+NbDUU5KkapZ6SlJ/6Grwi4jDI+LOiFgVESdXrJ8WEZeX65dHxNxy+YERcWv5892IeE032zlWjvhJklTN4CdJ/aFrwS8iBoDzgCOABcBxEbGgbbMTgIcyc0/gbOCscvn3gYWZuS9wOPCP5WWu+5LBT5Kkas7xk6T+0M0RvwOBVZl5V2Y+AVwGLGrbZhFwcXn7CuCwiIjMfCwzh3qI6UDHS1v3A0s9JUmq5hw/SeoP3Qx+s4F7W+6vLpdVblMGvfXATICIeHFErARuA97aEgT7jiN+kiRVs9RTkvpD317cJTOXZ+bewAHAKRExvX2biFgcESsiYsXatWt738iSwU+SpGoGP0nqD90MfvcBu7fcn1Muq9ymnMM3A1jXukFm3gE8SsXfLMrMJZm5MDMXzpo1q8ambx1LPSVJquYcP0nqD90MfjcC8yNiXkRMBY4FlrZtsxQ4vrx9FLAsM7PcZzJARDwHeD5wTxfbOiaO+EmSVM05fpLUH7p2pczMHIyIE4GrgAHgwsxcGRFnACsycylwAXBJRKwCHqQIhwAHASdHxEbgSeBtmfmLbrV1rAx+kiRVs9RTkvpDV/9EQmZeCVzZtuz0ltsbgKMr9rsEuKSbbavTUKmnwU+SpM0Z/CSpP/TtxV22J0Mjfs7xkyRpc87xk6T+YPCrgaWekiRVc46fJPUHg18NLPWUJKmapZ6S1B8MfjWw1FOSpGoGP0nqDwa/GljqKUlSNef4SVJ/MPjVwOAnSVI15/hJUn8w+NVgaI6fpZ6SJG3OUk9J6g8Gvxo44idJUjWDnyT1B4NfDQx+kiRVc46fJPUHg18NLPWUJKmac/wkqT8Y/GrgiJ8kSdUs9ZSk/mDwq4HBT5KkagY/SeoPBr8aWOopSVI1g58k9QeDXw0c8ZMkqZp9pCT1B4NfDezUJEmq5oifJPUHg18NLPWUJKmawU+S+oPBrwaO+EmSVM3gJ0n9weBXA4OfJEnV/APuktQfDH41sNRTkqRq/gF3SeoPBr8aOOInSVI1Sz0lqT8Y/Gpg8JMkqZrBT5L6g8GvBpZ6SpJUzTl+ktQfDH41cMRPkqRqzvGTpP5g8KuBwU+SpGqWekpSfzD41cBST0mSqhn8JKk/GPxq4IifJEnVnOMnSf3B4FcDg58kSdVa+8jMbLg1kjRxGfxqYPCTJKnapEmTnBIhSX3A4FcDOzRJkjpznp8kNc/gVwNH/CRJ6sx5fpLUPINfDQx+kiR15t/yk6TmGfxqYKmnJEmdWeopSc0z+NXAET9JUpWIODwi7oyIVRFxcsX6aRFxebl+eUTMbVl3Srn8zoh4Zcvy90TEyoj4fkR8ISKm9+jpbDODnyQ1z+BXA4OfJKldRAwA5wFHAAuA4yJiQdtmJwAPZeaewNnAWeW+C4Bjgb2Bw4F/iIiBiJgNvBNYmJn7AAPldn3NOX6S1DyDXw0i4qnb/o0iSVLpQGBVZt6VmU8AlwGL2rZZBFxc3r4COCyKTmURcFlmPp6ZdwOryuMBTAZ2iIjJwNOAn3X5eYyZc/wkqXkGvxpExFPz/OzUJEml2cC9LfdXl8sqt8nMQWA9MLPTvpl5H/BJ4KfAGmB9Zv5HV1pfI0s9Jal5Br+aWO4pSeq2iHgGxWjgPODZwI4R8foO2y6OiBURsWLt2rW9bOYWDH6S1DyDX028sqckqc19wO4t9+eUyyq3KUs3ZwDrhtn3D4G7M3NtZm4Evgz8ftWDZ+aSzFyYmQtnzZpVw9PZds7xk6TmGfxq4oifJKnNjcD8iJgXEVMpLsKytG2bpcDx5e2jgGVZTBZfChxbXvVzHjAf+A5FiedLIuJp5VzAw4A7evBcxsQ5fpLUvMlNN2C8MPhJklpl5mBEnAhcRXH1zQszc2VEnAGsyMylwAXAJRGxCniQ8gqd5XZfBG4HBoG3Z+YmYHlEXAHcXC6/BVjS6+e2tSz1lKTmGfxqYqmnJKldZl4JXNm27PSW2xuAozvseyZwZsXyvwX+tt6WdpfBT5KaZ6lnTRzxkySpmnP8JKl5Br+aGPwkSarmHD9Jap7BryaWekqSVM1ST0lqnsGvJo74SZJUzeAnSc0z+NXE4CdJUjXn+ElS8wx+NbHUU5Kkas7xk6TmGfxq4oifJEnVLPWUpOYZ/Gpi8JMkqZrBT5KaZ/CryVDws9RTkqTNOcdPkppn8KvJ0Bw/R/wkSdqcc/wkqXkGv5pY6ilJUjVLPSWpeQa/mljqKUlSNYOfJDXP4FcTSz0lSarmHD9Jap7BryaWekqSVM05fpLUPINfTQx+kiRVs9RTkppn8KvJUKmnc/wkSdqcwU+Smmfwq4kjfpIkVXOOnyQ1z+BXE4OfJEnVnOMnSc0z+NXEUk9JkqpZ6ilJzTP41cQRP0mSqhn8JKl5Br+aGPwkSarmHD9Jap7BryaWekqSVM0RP0lqnsGvJo74SZJUzYu7SFLzRhX8IuKS0SybyAx+kjR+2Q+OjSN+ktS80Y747d16JyIGgP3rb872y1JPSRrX7AfHwDl+ktS8YYNfRJwSEY8AL4iIX5Y/jwA/B/61Jy3cTjjiJ0njj/1gPRzxk6TmDRv8MvNjmbkz8InMfHr5s3NmzszMU3rUxu2CwU+Sxh/7wXo4x0+SmjfaUs+vRcSOABHx+oj4VEQ8p4vt2u5Y6ilJ45r94Bg44idJzRtt8Pss8FhEvBB4H/Bj4PNda9V2yBE/SRrX7AfHwDl+ktS80Qa/wcxMYBFwbmaeB+zcvWZtfwx+kjSu2Q+OgSN+ktS8yaPc7pGIOAX4S+DgiJgETOles7Y/Q8HPUk9JGpfsB8fAOX6S1LzRjvgdAzwOvDkz7wfmAJ/oWqu2Q0Nz/OzUJGlcsh8cA0f8JKl5owp+ZSd3KTAjIl4FbMhM5za0sNRTksYv+8GxcY6fJDVvVMEvIl4LfAc4GngtsDwijupmw7Y3lnpK0vhlPzg2jvhJUvNGO8fvVOCAzPw5QETMAv4TuGK4nSLicODTwABwfmZ+vG39NIqrou0PrAOOycx7IuKPgI8DU4EngPdn5rJRP6sGWOopSePaNvWDKjjHT5KaN9o5fpOGOrvSupH2jYgB4DzgCGABcFxELGjb7ATgoczcEzgbOKtc/gvg1Zn5e8DxwCWjbGdjLPWUpHFtq/tB/YYjfpLUvNGO+H09Iq4CvlDePwa4coR9DgRWZeZdABFxGcVlsG9v2WYR8OHy9hXAuRERmXlLyzYrgR0iYlpmPj7K9vacpZ6SNK5tSz+oksFPkpo3bPCLiD2B3TLz/RHx58BB5arrKSa5D2c2cG/L/dXAizttk5mDEbEemEkx4jfkvwE3V4W+iFgMLAbYY489RmhOd1nqKUnjzxj7QZW8uIskNW+kMpVzgF8CZOaXM/O9mfle4Cvluq6KiL0pyj//e9X6zFySmQszc+GsWbO63ZxhWeopSePSOTTYD44XzvGTpOaNFPx2y8zb2heWy+aOsO99wO4t9+eUyyq3iYjJwAyKeRNExByKjvUNmfnjER6rcZZ6StK4NJZ+UCVLPSWpeSMFv12GWbfDCPveCMyPiHkRMRU4Fljats1Siou3ABwFLMvMjIhdgH8DTs7Mb4/wOH3BUk9JGpd2GWbdSP2gSgY/SWreSMFvRUS8pX1hRPwVcNNwO2bmIHAicBVwB/DFzFwZEWdExJ+Vm10AzIyIVcB7gZPL5ScCewKnR8St5c8zR/2sGmCppySNS9vcD+o3nOMnSc0b6aqe7wa+EhGv4zcd3EKKv6/3mpEOnplX0nbVs8w8veX2Boo/htu+30eAj4x0/H5i8JOkcendjKEfVME5fpLUvGGDX2Y+APx+RLwc2Kdc/G/9/sfUmzBU6ukcP0kaP+wH62GppyQ1b1R/xy8zrwau7nJbtmuO+EnS+LWt/WBEHA58GhgAzs/Mj7etnwZ8Htif4uJmx2TmPeW6U4ATgE3AOzPzqnL5LsD5FEE0gTdn5vXb9MR6xOAnSc0baY6fRsngJ0lqFREDwHnAEcAC4LiIWNC22QnAQ5m5J3A2xZ8wotzuWGBv4HDgH8rjQREkv56ZzwdeSDGPvq85x0+Smmfwq4mlnpKkNgcCqzLzrsx8ArgMWNS2zSLg4vL2FcBhERHl8ssy8/HMvBtYBRwYETOAQygujkZmPpGZD3f/qYyNc/wkqXkGv5o44idJajMbuLfl/upyWeU25dWw1wMzh9l3HrAW+KeIuCUizo+IHasePCIWR8SKiFixdu3aOp7PNrPUU5KaZ/CricFPktQDk4H9gM9m5ouAX/GbP4W0mcxckpkLM3PhrFmzetnGLRj8JKl5Br+aWOopSWpzH7B7y/055bLKbSJiMjCD4iIvnfZdDazOzOXl8isogmBfc46fJDXP4FcTR/wkSW1uBOZHxLyImEpxsZalbdssBY4vbx8FLMvMLJcfGxHTImIeMB/4TmbeD9wbEb9b7nMYcHu3n8hYOcdPkpo3qj/noJEZ/CRJrTJzMCJOBK6i+HMOF2bmyog4A1iRmUspLtJySUSsAh6kCIeU232RItQNAm/PzKEO5h3ApWWYvAt4U0+f2Daw1FOSmmfwq8lQ8LPUU5I0JDOvBK5sW3Z6y+0NwNEd9j0TOLNi+a3Awlob2mUGP0lqnqWeNRma4+eInyRJm3OOnyQ1z+BXE0s9JUmqNmnSJIo/T2hljCQ1xeBXE0s9JUnqzHJPSWqWwa8mlnpKktSZwU+SmmXwq4mlnpIkdeY8P0lqlsGvJpZ6SpLUmX/LT5KaZfCriaWekiR1ZqmnJDXL4FcTSz0lSerM4CdJzTL41cRST0mSOnOOnyQ1y+BXE0s9JUnqzDl+ktQsg19NLPWUJKkzSz0lqVkGv5pY6ilJUmcGP0lqlsGvJpZ6SpLUmXP8JKlZBr+aWOopSVJnzvGTpGYZ/Gpi8JMkqTNLPSWpWQa/mgyVejrHT5KkLRn8JKlZBr+aOOInSVJnzvGTpGYZ/Gpi8JMkqTNH/CSpWQa/mljqKUlSZ17cRZKaZfCriSN+kiR15oifJDXL4FcTg58kSZ05x0+SmmXwq8lQh2appyRJW3LET5KaZfCrydAcP0f8JEnaknP8JKlZBr+aWOopSVJnjvhJUrMMfjWx1FOSpM6c4ydJzTL41cRST0mSOnPET5KaZfCriaWekiR15hw/SWqWwa8mlnpKktSZI36S1CyDX00s9ZQkqTPn+ElSswx+NbHUU5Kkzhzxk6RmGfxqYqmnJEmdOcdPkppl8KuJpZ6SJHXmiJ8kNcvgVxNLPSVJ6sw5fpLULINfTSz1lCSpM0f8JKlZBr+aWOopSVJnzvGTpGYZ/GrSOuKXmQ23RpKk/uKInyQ1y+BXk4ggIgAMfpIktXGOnyQ1y+BXI8s9JUmq5oifJDXL4Fcjr+wpSVI15/hJUrMMfjXyyp6SJFVzxE+SmmXwq5GlnpIkVXOOnyQ1y+BXI0s9JUmq5oifJDXL4Fcjg58kSdWc4ydJzTL41cg5fpKkVhFxeETcGRGrIuLkivXTIuLycv3yiJjbsu6UcvmdEfHKtv0GIuKWiPhaD55GLYaC38aNGxtuiSRNTAa/GjnHT5I0JCIGgPOAI4AFwHERsaBtsxOAhzJzT+Bs4Kxy3wXAscDewOHAP5THG/Iu4I7uPoN6TZ06FYAnnnii4ZZI0sRk8KuRpZ6SpBYHAqsy867MfAK4DFjUts0i4OLy9hXAYRER5fLLMvPxzLwbWFUej4iYA/wpcH4PnkNtpk+fDsCGDRsabokkTUwGvxpZ6ilJajEbuLfl/upyWeU2mTkIrAdmjrDvOcDfANtVZ7PDDjsA8Otf/7rhlkjSxGTwq5GlnpKkboqIVwE/z8ybRrHt4ohYEREr1q5d24PWDc8RP0lqlsGvRpZ6SpJa3Afs3nJ/TrmscpuImAzMANYNs+8fAH8WEfdQlI6+IiL+uerBM3NJZi7MzIWzZs0a+7MZI0f8JKlZBr8aWeopSWpxIzA/IuZFxFSKi7UsbdtmKXB8efsoYFlmZrn82PKqn/OA+cB3MvOUzJyTmXPL4y3LzNf34smMlSN+ktSsyU03YDyx1FOSNCQzByPiROAqYAC4MDNXRsQZwIrMXApcAFwSEauABynCHOV2XwRuBwaBt2fmdt25DI34GfwkqRkGvxpZ6ilJapWZVwJXti07veX2BuDoDvueCZw5zLGvAa6po529MDTiZ6mnJDXDUs8aWeopSVI1Sz0lqVkGvxpZ6ilJUjUv7iJJzTL41chST0mSqjniJ0nNMvjVyFJPSZKqTZkyhUmTJjE4OMjg4GDTzZGkCcfgVyNLPSVJqhYRjvpJUoMMfjWy1FOSpM4MfpLUHINfjSz1lCSpMy/wIknNMfjVyFJPSZI6c8RPkppj8KuRpZ6SJHXmiJ8kNcfgVyNLPSVJ6swRP0lqjsGvRpZ6SpLUmcFPkppj8KuRpZ6SJHVmqackNcfgVyNLPSVJ6swRP0lqTleDX0QcHhF3RsSqiDi5Yv20iLi8XL88IuaWy2dGxNUR8WhEnNvNNtbJET9JkjpzxE+SmtO14BcRA8B5wBHAAuC4iFjQttkJwEOZuSdwNnBWuXwDcBpwUrfa1w3O8ZMkqTNH/CSpOd0c8TsQWJWZd2XmE8BlwKK2bRYBF5e3rwAOi4jIzF9l5rcoAuB2w1JPSZI6GxrxM/hJUu91M/jNBu5tub+6XFa5TWYOAuuBmaN9gIhYHBErImLF2rVrx9jcsbPUU5KkzoZG/Cz1lKTe264v7pKZSzJzYWYunDVrVtPNsdRTkqRhWOopSc3pZvC7D9i95f6cclnlNhExGZgBrOtim7rKET9Jkjrz4i6S1JxuBr8bgfkRMS8ipgLHAkvbtlkKHF/ePgpYlpnZxTZ1lXP8JEnqzBE/SWrO5G4dODMHI+JE4CpgALgwM1dGxBnAisxcClwAXBIRq4AHKcIhABFxD/B0YGpEHAn8cWbe3q321sFST0mSOnPET5Ka07XgB5CZVwJXti07veX2BuDoDvvO7WbbusFST0mSOnPET5Kas11f3KXfWOopSVJnBj9Jao7Br0aWekqS1JmlnpLUHINfjSz1lCSpM0f8JKk5Br8aWeopSVJnjvhJUnMMfjWy1FOSpM4c8ZOk5hj8amSppyRJnQ2N+Bn8JKn3DH41stRTkqTOhkb8LPWUpN4z+NXIUk9Jkjqz1FOSmmPwq5GlnpIkdebFXSSpOQa/GlnqKUlSZ474SVJzDH41stRTkqTOHPGTpOYY/GpkqackSZ1NmzYNgMcff5zMbLg1kjSxGPxqZKmnJEmdTZo0ialTpwJF+JMk9Y7Br0aWekqSNDzLPSWpGQa/GlnqKUnS8LzAiyQ1w+BXI0s9JUkaniN+ktQMg1+NHPGTJGl4jvhJUjMMfjVyjp8kScMbGvEz+ElSbxn8amSppyRJwxsa8bPUU5J6y+BXI0s9JUkanqWektQMg1+NLPWUJGl4XtxFkpph8KuRpZ6SJA3PET9JaobBr0aWekqSWkXE4RFxZ0SsioiTK9ZPi4jLy/XLI2Juy7pTyuV3RsQry2W7R8TVEXF7RKyMiHf18OnUwhE/SWqGwa9GlnpKkoZExABwHnAEsAA4LiIWtG12AvBQZu4JnA2cVe67ADgW2Bs4HPiH8niDwPsycwHwEuDtFcfsa474SVIzDH41csRPktTiQGBVZt6VmU8AlwGL2rZZBFxc3r4COCwiolx+WWY+npl3A6uAAzNzTWbeDJCZjwB3ALN78FxqY/CTpGYY/GrkHD9JUovZwL0t91ezZUh7apvMHATWAzNHs29ZFvoiYHnVg0fE4ohYEREr1q5du+3PomaWekpSMwx+NbLUU5LUCxGxE/Al4N2Z+cuqbTJzSWYuzMyFs2bN6m0Dh+GInyQ1w+BXI0s9JUkt7gN2b7k/p1xWuU1ETAZmAOuG2zciplCEvksz88tdaXkXOeInSc0w+NXIUk9JUosbgfkRMS8iplJcrGVp2zZLgePL20cByzIzy+XHllf9nAfMB75Tzv+7ALgjMz/Vk2dRM0f8JKkZk5tuwHhiqackaUhmDkbEicBVwABwYWaujIgzgBWZuZQixF0SEauABynCIeV2XwRup7iS59szc1NEHAT8JXBbRNxaPtQHM/PKnj65MTD4SVIzDH41stRTktSqDGRXti07veX2BuDoDvueCZzZtuxbQNTf0t6x1FOSmmGpZ40s9ZQkaXiO+ElSMwx+NbLUU5Kk4TniJ0nNMPjVyFJPSZKG54ifJDXD4FcjSz0lSRqeI36S1AyDX40s9ZQkaXiO+ElSMwx+NbLUU5Kk4Rn8JKkZBr8aWeopSdLwLPWUpGYY/GrkiJ8kScNzxE+SmmHwq5Fz/CRJGp4jfpLUDINfjSz1lCRpeI74SVIzDH41stRTkqThGfwkqRkGvxpZ6ilJ0vCmTJnCwMAAmzZtYuPGjU03R5ImDINfjSz1lCRpZI76SVLvGfxqZKmnJEkj8wIvktR7Br8aWeopSdLIHPGTpN4z+NXIUk9JkkbmiJ8k9Z7Br0aWekqSNDJH/CSp9wx+NbLUU5KkkRn8JKn3DH41stRTkqSRWeopSb1n8KuRpZ6SJI3MET9J6j2DX40s9ZQkaWSO+ElS7xn8auSInyRJI3PET5J6z+BXI+f4SZI0MoOfJPWewa9GlnpKkjQySz0lqfcMfjWy1FOSpJE54idJvWfwq5GlnpIkjcwRP0nqPYNfjSICgMwkMxtujSRJ/ckRP0nqPYNfjSLCeX6SJI3AET9J6j2DX80s95QkaXiO+ElS7xn8auYFXiRJGp7BT5J6z+BXM0s9JUkanqWektR7Br+aWeopSdLwHPGTpN4z+NXMUk9JkobniJ8k9d7kphsw3gyVer7sZS9j8uRtP7077bQTH/nIRzjkkEPqapokSX3BET9J6j2DX81+93d/l+uvv57bbrttzMd6zWtewy233MIee+xRQ8skSeoPBj9J6j2DX82WLVvG7bffPubjfOhDH+Lf//3fee1rX8u1117L1KlTa2idJEnNs9RTknrP4Fez6dOns99++435OJdccgn77bcfy5cv5/3vfz+f/vSna2idJEnNc8RPknrP4NenZs6cyRe/+EUOPvhgPvOZz/D85z+/lkA5Ws997nPZdddde/Z4kqSJwxE/Seo9g18fe/GLX8wnP/lJ3vWud/G2t72tp4+92267sXLlSmbOnNnTx5UkjX+O+ElS7xn8+tw73vEO1q9fz9e+9rWePebq1av52c9+xqmnnsrnPve5nj2uJGliGAp+jvhJUu9EZjbdhlosXLgwV6xY0XQzxoU77riDF7zgBWzatInly5dzwAEHNN0kSdpMRNyUmQubbsf2ot/6yA0bNrDDDjswdepUHn/88aabI0njxnD9o3/AXVvYa6+9eM973kNm8va3v50nn3yy6SZJksaRadOmAfDEE0/Yx0hSjxj8VOm0005j9uzZ3HjjjVxwwQVNN0eSNI5EhPP8JKnHujrHLyIOBz4NDADnZ+bH29ZPAz4P7A+sA47JzHvKdacAJwCbgHdm5lXdbKs2t/POO/OpT32KY445hpNPPpnBwUEiYquOMX36dBYtWsQznvGMLrVSkvpbN/rBkY65vZg+fTobNmxgw4YNPO1pT2u6OZI07nUt+EXEAHAe8EfAauDGiFiama1/3fwE4KHM3DMijgXOAo6JiAXAscDewLOB/4yI52Xmpm61V1s6+uijWbJkCd/4xje2+aqiM2bM4KSTTuJd73oXO++8c80tlKT+1Y1+sNxnpGNuF3bYYQcefvhhFi5cyOTJw/86EhHMmTOH+fPnM3/+fJ71rGd1/DJyxowZ7LPPPuy+++5b/YWlJI1n3RzxOxBYlZl3AUTEZcAioLVzWgR8uLx9BXBuFJ/Si4DLMvNx4O6IWFUe7/outldtIoKLLrqIT37yk9tUivODH/yAb37zm5x22mmcc845vPrVr2ZgYKALLe0PEcGkSZOYNGkSAwMDTJ48mSlTpjBlyhQmTWqmqnrol55e/fLT68er0/bY5u3Vy1/+cg455JCmm9EL3egHGcUxtwv77rsva9as4e677x7V9j/84Q9ZtmzZqI8/Y8YM9tprL3bcccenlkUEkydPfuqn9f/9lClT2Hnnndl5553Zaaedtuiv/IyQ1AunnnrqiF+GbatuBr/ZwL0t91cDL+60TWYORsR6YGa5/Ia2fWd3r6nqZM6cOZxzzjnbvP/VV1/Naaedxre//W0uuuii2tolafs1MDAwUYJft/rBkY65XVi6dCl33XXXqLYdHBzknnvu4Uc/+hE/+tGPWLduXcdtf/7zn3Pbbbexdu1abrjhho7bSVI/+sAHPrBdBr+ui4jFwGKAPfbYo+HWqMrLX/5yrrvuOr75zW+yatWqppvTVZnJk08+yaZNm9i0aRODg4Ns3LiRjRs30sSfTRl6zF49dq8fr07bY5u3ZwcffHDTTZgQ+r2PnDx5Ms973vNG3rC0YMGCrTr+Aw88wA9+8AM2btz41LKhz+ihz+dWTzzxBI888shTP62fC35GSOqVblbHdTP43Qfs3nJ/TrmsapvVETEZmEExuX00+5KZS4AlUPyNotparlpFBIceeiiHHnpo002RpF7qVj84Yv8I9pG77bYbu+22W9PNkKS+0c2JRzcC8yNiXkRMpZikvrRtm6XA8eXto4BlWXytthQ4NiKmRcQ8YD7wnS62VZKkunWjHxzNMSVJ2kLXRvzKuQonAldRXHL6wsxcGRFnACsycylwAXBJOWn9QYoOjHK7L1JMVh8E3u4VPSVJ25Nu9YNVx+z1c5MkbX9ivNStL1y4MFesWNF0MyRJPRARN2Xmwqbbsb2wj5SkiWG4/rGZa8xLkiRJknrG4CdJkiRJ45zBT5IkSZLGOYOfJEmSJI1zBj9JkiRJGucMfpIkSZI0zhn8JEmSJGmcM/hJkiRJ0jhn8JMkSZKkcc7gJ0mSJEnjnMFPkiRJksY5g58kSZIkjXORmU23oRYRsRb4SQ2H2hX4RQ3HGU88J9U8L9U8L9U8L9W29bw8JzNn1d2Y8aqmPtL3cDXPSzXPSzXPSzXPS7VtOS8d+8dxE/zqEhErMnNh0+3oJ56Tap6Xap6Xap6Xap6X7YevVTXPSzXPSzXPSzXPS7W6z4ulnpIkSZI0zhn8JEmSJGmcM/htaUnTDehDnpNqnpdqnpdqnpdqnpfth69VNc9LNc9LNc9LNc9LtVrPi3P8JEmSJGmcc8RPkiRJksY5g58kSZIkjXMGv1JEHB4Rd0bEqog4uen2NCUido+IqyPi9ohYGRHvKpf/VkT8v4j4UfnvM5puaxMiYiAibomIr5X350XE8vJ9c3lETG26jb0WEbtExBUR8YOIuCMiXjrR3y8R8Z7y/8/3I+ILETF9or5XIuLCiPh5RHy/ZVnl+yMKnynP0fciYr/mWq5W9pH2jyOxf9yS/WM1+8hCE/2jwY/iwwo4DzgCWAAcFxELmm1VYwaB92XmAuAlwNvLc3Ey8I3MnA98o7w/Eb0LuKPl/lnA2Zm5J/AQcEIjrWrWp4GvZ+bzgRdSnJ8J+36JiNnAO4GFmbkPMAAcy8R9r1wEHN62rNP74whgfvmzGPhsj9qoYdhHPsX+cXj2j1uyf2xjH7mZi+hx/2jwKxwIrMrMuzLzCeAyYFHDbWpEZq7JzJvL249QfEjNpjgfF5ebXQwc2UgDGxQRc4A/Bc4v7wfwCuCKcpMJd14iYgZwCHABQGY+kZkP4/tlMrBDREwGngasYYK+VzLzWuDBtsWd3h+LgM9n4QZgl4h4Vk8aquHYR2L/OBz7xy3ZPw7LPpJm+keDX2E2cG/L/dXlsgktIuYCLwKWA7tl5ppy1f3Abk21q0HnAH8DPFnenwk8nJmD5f2J+L6ZB6wF/qks8Tk/InZkAr9fMvM+4JPATyk6s/XATfheadXp/eFncX/ydWlj/7iFc7B/bGf/WME+ckRd7R8NfqoUETsBXwLenZm/bF2Xxd8AmVB/ByQiXgX8PDNvarotfWYysB/w2cx8EfAr2spWJtr7pazHX0TR6T8b2JEtSzlUmmjvD23/7B83Z//Ykf1jBfvI0evG+8PgV7gP2L3l/pxy2YQUEVMoOrVLM/PL5eIHhoaUy39/3lT7GvIHwJ9FxD0UZU6voKjd36UsVYCJ+b5ZDazOzOXl/SsoOrqJ/H75Q+DuzFybmRuBL1O8fyb6e6VVp/eHn8X9ydelZP9Yyf6xmv1jNfvI4XW1fzT4FW4E5pdXFJpKMcl0acNtakRZl38BcEdmfqpl1VLg+PL28cC/9rptTcrMUzJzTmbOpXh/LMvM1wFXA0eVm03E83I/cG9E/G656DDgdib2++WnwEsi4mnl/6ehczKh3yttOr0/lgJvKK9e9hJgfUvJi5pjH4n9Yyf2j9XsHzuyjxxeV/vHKEYRFRF/QlGjPgBcmJlnNtuiZkTEQcB1wG38plb/gxTzGL4I7AH8BHhtZrZPSJ0QIuJQ4KTMfFVE/A7FN5y/BdwCvD4zH2+weT0XEftSTOifCtwFvIniS6UJ+36JiL8DjqG4CuAtwF9R1OJPuPdKRHwBOBTYFXgA+Fvgq1S8P8pfAs6lKPt5DHhTZq5ooNlqYx9p/zga9o+bs3+sZh9ZaKJ/NPhJkiRJ0jhnqackSZIkjXMGP0mSJEka5wx+kiRJkjTOGfwkSZIkaZwz+EmSJEnSOGfwk3ogIh4t/50bEX9R87E/2Hb/v+o8viRJ3WL/KPWOwU/qrbnAVnVsETF5hE0269gy8/e3sk2SJDVtLvaPUlcZ/KTe+jhwcETcGhHviYiBiPhERNwYEd+LiP8OxR/BjYjrImIpcHu57KsRcVNErIyIxeWyjwM7lMe7tFw29O1plMf+fkTcFhHHtBz7moi4IiJ+EBGXln8YlIj4eETcXrblkz0/O5Kkicr+Ueqykb4pkVSvk4GTMvNVAGUHtT4zD4iIacC3I+I/ym33A/bJzLvL+2/OzAcjYgfgxoj4UmaeHBEnZua+FY/158C+wAuBXct9ri3XvQjYG/gZ8G3gDyLiDuA1wPMzMyNil3qfuiRJHdk/Sl3miJ/UrD8G3hARtwLLgZnA/HLdd1o6NYB3RsR3gRuA3Vu26+Qg4AuZuSkzHwC+CRzQcuzVmfkkcCtFic16YANwQUT8OfDYGJ+bJEnbyv5RqpnBT2pWAO/IzH3Ln3mZOfSN5q+e2ijiUOAPgZdm5guBW4DpY3jcx1tubwImZ+YgcCBwBfAq4OtjOL4kSWNh/yjVzOAn9dYjwM4t968C/joipgBExPMiYseK/WYAD2XmYxHxfOAlLes2Du3f5jrgmHKexCzgEOA7nRoWETsBMzLzSuA9FCUwkiT1gv2j1GXO8ZN663vAprIk5SLg0xRlJDeXE8jXAkdW7Pd14K3lPIM7KcpZhiwBvhcRN2fm61qWfwV4KfBdIIG/ycz7y46xys7Av0bEdIpvWt+7Tc9QkqStZ/8odVlkZtNtkCRJkiR1kaWekiRJkjTOGfwkSZIkaZwz+EmSJEnSOGfwkyRJkqRxzuAnSZIkSeOcwU+SJEmSxjmDnyRJkiSNc/8fuLkUVEj0He4AAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig, (ax, ax_h) = plt.subplots(ncols=2, nrows=1)\n",
    "fig.set_size_inches(15,7)\n",
    "plot_cost_history(ax=ax, cost_history=optimizer_without_handle.cost_history)\n",
    "plot_cost_history(ax=ax_h, cost_history=optimizer_with_handle.cost_history)\n",
    "ax.set_title(\"Cost history without inertia decay\")\n",
    "ax_h.set_title(\"Cost history with exponential intertia decay\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "source": [
    "The rapid decay of the inertia weight contributes significantly to the overall best cost and position. It also converges a lot faster.\n",
    "\n",
    "The next part shows the explanation for this with an animation"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Comparing animations\n",
    "The `plotters` module offers two methods to perform animation, `plot_contour()`. This method plot the particles in a 2-D space.\n",
    "\n",
    "The objective function contours are added using the `Mesher` class.\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "from pyswarms.utils.plotters.formatters import Mesher\n",
    "# Initialize mesher with sphere function\n",
    "m = Mesher(func=fx.sphere)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Plotting in 2-D space\n",
    "\n",
    "We can obtain the swarm's position history using the `pos_history` attribute from the `optimizer` instance. To plot a 2D-contour, simply pass this together with the `Mesher` to the `plot_contour()` function. In addition, we can also mark the global minima of the sphere function, `(0,0)`, to visualize the swarm's \"target\"."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "2020-12-11 19:23:22,596 - matplotlib.animation - WARNING - MovieWriter imagemagick unavailable; using Pillow instead.\n",
      "2020-12-11 19:23:22,597 - matplotlib.animation - INFO - Animation.save using <class 'matplotlib.animation.PillowWriter'>\n",
      "2020-12-11 19:23:30,971 - matplotlib.animation - WARNING - MovieWriter imagemagick unavailable; using Pillow instead.\n",
      "2020-12-11 19:23:30,973 - matplotlib.animation - INFO - Animation.save using <class 'matplotlib.animation.PillowWriter'>\n"
     ]
    }
   ],
   "source": [
    "%%capture\n",
    "\n",
    "# Make and save animation\n",
    "animation = plot_contour(pos_history=optimizer_without_handle.pos_history,\n",
    "                         mesher=m,\n",
    "                         mark=(0,0))\n",
    "animation_h = plot_contour(pos_history=optimizer_with_handle.pos_history,\n",
    "                         mesher=m,\n",
    "                         mark=(0,0))\n",
    "# Enables us to view it in a Jupyter notebook\n",
    "animation.save('ani.gif', writer='imagemagick', fps=10)\n",
    "\n",
    "animation_h.save('ani_h.gif', writer='imagemagick', fps=10)\n",
    "\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "source": [
    "Compare the two animations. Observe the convergence time and particle overshoot in both figures.\n",
    "\n",
    "Left: Without handle\n",
    "\n",
    "Right: With handle\n",
    "\n",
    "<img src=\"ani.gif\" width=\"450\" align=\"left\">\n",
    "<img src=\"ani_h.gif\" width=\"450\" align=\"right\">\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Customizing ending options\n",
    "\n",
    "As of the current version(1.2.0), you'll need to create your own optimization loop to keep custom ending options.\n",
    "The next block shows a basic implementation of this without logging etc."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [
    "from pyswarms.backend.operators import compute_pbest, compute_objective_function"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "source": [
    "def optimize(objective_func, maxiters, oh_strategy,start_opts, end_opts):\n",
    "    opt = ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=start_opts, oh_strategy=oh_strategy)\n",
    "\n",
    "    swarm = opt.swarm\n",
    "    opt.bh.memory = swarm.position\n",
    "    opt.vh.memory = swarm.position\n",
    "    swarm.pbest_cost = np.full(opt.swarm_size[0], np.\n",
    "    inf)\n",
    "\n",
    "    for i in range(maxiters):\n",
    "        # Compute cost for current position and personal best\n",
    "        swarm.current_cost =  compute_objective_function(swarm, objective_func)\n",
    "        swarm.pbest_pos, swarm.pbest_cost = compute_pbest(swarm)\n",
    "\n",
    "        # Set best_cost_yet_found for ftol\n",
    "        best_cost_yet_found = swarm.best_cost\n",
    "        swarm.best_pos, swarm.best_cost = opt.top.compute_gbest(swarm)\n",
    "        # Perform options update\n",
    "        swarm.options = opt.oh( opt.options, iternow=i, itermax=maxiters, end_opts=end_opts )\n",
    "        print(\"Iteration:\", i,\" Options: \", swarm.options)    # print to see variation\n",
    "        # Perform velocity and position updates\n",
    "        swarm.velocity = opt.top.compute_velocity(\n",
    "            swarm, opt.velocity_clamp, opt.vh, opt.bounds\n",
    "        )\n",
    "        swarm.position = opt.top.compute_position(\n",
    "            swarm, opt.bounds, opt.bh\n",
    "        )\n",
    "    # Obtain the final best_cost and the final best_position\n",
    "    final_best_cost = swarm.best_cost.copy()\n",
    "    final_best_pos = swarm.pbest_pos[\n",
    "        swarm.pbest_cost.argmin()\n",
    "    ].copy()\n",
    "    return final_best_cost, final_best_pos"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 10,
   "outputs": []
  },
  {
   "source": [
    "In the next cell, you can play around with the start and end options, maximum iterations and the function itself to compare the outputs like above."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Iteration: 0  Options:  {'c1': 2.5, 'c2': 0.5, 'w': 0.8154845485377135}\nIteration: 1  Options:  {'c1': 2.476024064289623, 'c2': 0.52, 'w': 0.7638427274927154}\nIteration: 2  Options:  {'c1': 2.4520965166602724, 'c2': 0.54, 'w': 0.7212425273766464}\nIteration: 3  Options:  {'c1': 2.428217751727513, 'c2': 0.56, 'w': 0.6855550181382926}\nIteration: 4  Options:  {'c1': 2.4043881714225273, 'c2': 0.5800000000000001, 'w': 0.6552602432446853}\nIteration: 5  Options:  {'c1': 2.3806081852052783, 'c2': 0.6000000000000001, 'w': 0.6292465903435571}\nIteration: 6  Options:  {'c1': 2.3568782102861965, 'c2': 0.6200000000000001, 'w': 0.6066838570323415}\nIteration: 7  Options:  {'c1': 2.3331986718568167, 'c2': 0.6399999999999999, 'w': 0.5869404779457066}\nIteration: 8  Options:  {'c1': 2.3095700033298305, 'c2': 0.6599999999999999, 'w': 0.5695280957195421}\nIteration: 9  Options:  {'c1': 2.285992646589043, 'c2': 0.6799999999999999, 'w': 0.5540635587607113}\nIteration: 10  Options:  {'c1': 2.2624670522497583, 'c2': 0.7, 'w': 0.5402423141269194}\nIteration: 11  Options:  {'c1': 2.2389936799301475, 'c2': 0.72, 'w': 0.527819424452714}\nIteration: 12  Options:  {'c1': 2.215572998534194, 'c2': 0.74, 'w': 0.5165957922398924}\nIteration: 13  Options:  {'c1': 2.192205486546836, 'c2': 0.76, 'w': 0.5064080078932764}\nIteration: 14  Options:  {'c1': 2.1688916323420004, 'c2': 0.78, 'w': 0.4971207626134709}\nIteration: 15  Options:  {'c1': 2.1456319345042183, 'c2': 0.8, 'w': 0.4886211049862233}\nIteration: 16  Options:  {'c1': 2.1224269021646167, 'c2': 0.8200000000000001, 'w': 0.48081404179727616}\nIteration: 17  Options:  {'c1': 2.0992770553520845, 'c2': 0.8400000000000001, 'w': 0.4736191317674961}\nIteration: 18  Options:  {'c1': 2.076182925360504, 'c2': 0.8600000000000001, 'w': 0.46696782158333405}\nIteration: 19  Options:  {'c1': 2.053145055132976, 'c2': 0.8799999999999999, 'w': 0.4608013430638035}\nIteration: 20  Options:  {'c1': 2.030163999664059, 'c2': 0.8999999999999999, 'w': 0.455069038916464}\nIteration: 21  Options:  {'c1': 2.007240326421086, 'c2': 0.9199999999999999, 'w': 0.44972701900111317}\nIteration: 22  Options:  {'c1': 1.984374615785726, 'c2': 0.94, 'w': 0.4447370737567352}\nIteration: 23  Options:  {'c1': 1.961567461517037, 'c2': 0.96, 'w': 0.4400657894042114}\nIteration: 24  Options:  {'c1': 1.938819471237338, 'c2': 0.98, 'w': 0.4356838227118487}\nIteration: 25  Options:  {'c1': 1.916131266942353, 'c2': 1.0, 'w': 0.43156530287330336}\nIteration: 26  Options:  {'c1': 1.893503485537166, 'c2': 1.02, 'w': 0.4276873353495389}\nIteration: 27  Options:  {'c1': 1.87093677939967, 'c2': 1.04, 'w': 0.4240295880363697}\nIteration: 28  Options:  {'c1': 1.8484318169733072, 'c2': 1.06, 'w': 0.4205739443113132}\nIteration: 29  Options:  {'c1': 1.8259892833910558, 'c2': 1.08, 'w': 0.4173042107280646}\nIteration: 30  Options:  {'c1': 1.8036098811327728, 'c2': 1.1, 'w': 0.41420586961014694}\nIteration: 31  Options:  {'c1': 1.7812943307181757, 'c2': 1.12, 'w': 0.41126586872702486}\nIteration: 32  Options:  {'c1': 1.759043371437939, 'c2': 1.14, 'w': 0.4084724417486748}\nIteration: 33  Options:  {'c1': 1.7368577621255956, 'c2': 1.16, 'w': 0.40581495436664605}\nIteration: 34  Options:  {'c1': 1.7147382819731596, 'c2': 1.18, 'w': 0.4032837719146377}\nIteration: 35  Options:  {'c1': 1.6926857313936474, 'c2': 1.2, 'w': 0.4008701450750272}\nIteration: 36  Options:  {'c1': 1.6707009329339555, 'c2': 1.22, 'w': 0.39856611086172655}\nIteration: 37  Options:  {'c1': 1.6487847322418678, 'c2': 1.24, 'w': 0.39636440655637023}\nIteration: 38  Options:  {'c1': 1.626937999091311, 'c2': 1.26, 'w': 0.3942583946688905}\nIteration: 39  Options:  {'c1': 1.6051616284703591, 'c2': 1.28, 'w': 0.3922419973141236}\nIteration: 40  Options:  {'c1': 1.583456541736921, 'c2': 1.3, 'w': 0.3903096386581006}\nIteration: 41  Options:  {'c1': 1.5618236878475174, 'c2': 1.32, 'w': 0.3884561943027294}\nIteration: 42  Options:  {'c1': 1.5402640446650828, 'c2': 1.34, 'w': 0.3866769466548326}\nIteration: 43  Options:  {'c1': 1.518778620352329, 'c2': 1.36, 'w': 0.3849675454721789}\nIteration: 44  Options:  {'c1': 1.497368454857856, 'c2': 1.38, 'w': 0.3833239729009879}\nIteration: 45  Options:  {'c1': 1.4760346215029587, 'c2': 1.4, 'w': 0.38174251242096996}\nIteration: 46  Options:  {'c1': 1.454778228677894, 'c2': 1.42, 'w': 0.3802197211989471}\nIteration: 47  Options:  {'c1': 1.4336004216573355, 'c2': 1.44, 'w': 0.3787524054234573}\nIteration: 48  Options:  {'c1': 1.4125023845457787, 'c2': 1.46, 'w': 0.37733759825283403}\nIteration: 49  Options:  {'c1': 1.39148534236489, 'c2': 1.48, 'w': 0.3759725400600326}\nIteration: 50  Options:  {'c1': 1.3705505632961241, 'c2': 1.5, 'w': 0.3746546607005046}\nIteration: 51  Options:  {'c1': 1.349699361093501, 'c2': 1.52, 'w': 0.3733815635660021}\nIteration: 52  Options:  {'c1': 1.3289330976831786, 'c2': 1.54, 'w': 0.3721510112183664}\nIteration: 53  Options:  {'c1': 1.3082531859684736, 'c2': 1.56, 'w': 0.3709609124240106}\nIteration: 54  Options:  {'c1': 1.2876610928612768, 'c2': 1.58, 'w': 0.3698093104326385}\nIteration: 55  Options:  {'c1': 1.2671583425634432, 'c2': 1.6, 'w': 0.36869437236336694}\nIteration: 56  Options:  {'c1': 1.2467465201247816, 'c2': 1.62, 'w': 0.3676143795783189}\nIteration: 57  Options:  {'c1': 1.226427275307758, 'c2': 1.6400000000000001, 'w': 0.36656771893834633}\nIteration: 58  Options:  {'c1': 1.2062023267930964, 'c2': 1.6600000000000001, 'w': 0.36555287484817117}\nIteration: 59  Options:  {'c1': 1.1860734667651598, 'c2': 1.6800000000000002, 'w': 0.3645684220091819}\nIteration: 60  Options:  {'c1': 1.1660425659214986, 'c2': 1.7, 'w': 0.3636130188076487}\nIteration: 61  Options:  {'c1': 1.146111578957366, 'c2': 1.72, 'w': 0.36268540127440874}\nIteration: 62  Options:  {'c1': 1.126282550583548, 'c2': 1.74, 'w': 0.36178437755931375}\nIteration: 63  Options:  {'c1': 1.1065576221447462, 'c2': 1.76, 'w': 0.3609088228700637}\nIteration: 64  Options:  {'c1': 1.0869390389162645, 'c2': 1.78, 'w': 0.360057674830598}\nIteration: 65  Options:  {'c1': 1.0674291581692645, 'c2': 1.8, 'w': 0.35922992921908464}\nIteration: 66  Options:  {'c1': 1.0480304581097744, 'c2': 1.8199999999999998, 'w': 0.35842463604983676}\nIteration: 67  Options:  {'c1': 1.0287455478145502, 'c2': 1.8399999999999999, 'w': 0.3576408959672543}\nIteration: 68  Options:  {'c1': 1.0095771783084766, 'c2': 1.8599999999999999, 'w': 0.3568778569232281}\nIteration: 69  Options:  {'c1': 0.9905282549543739, 'c2': 1.88, 'w': 0.3561347111123839}\nIteration: 70  Options:  {'c1': 0.9716018513579736, 'c2': 1.9, 'w': 0.35541069214215554}\nIteration: 71  Options:  {'c1': 0.9528012250299461, 'c2': 1.92, 'w': 0.35470507241699134}\nIteration: 72  Options:  {'c1': 0.9341298350951458, 'c2': 1.94, 'w': 0.35401716071805106}\nIteration: 73  Options:  {'c1': 0.9155913623992082, 'c2': 1.96, 'w': 0.3533462999615839}\nIteration: 74  Options:  {'c1': 0.8971897324376921, 'c2': 1.98, 'w': 0.35269186512080497}\nIteration: 75  Options:  {'c1': 0.8789291416275995, 'c2': 2.0, 'w': 0.35205326129754305}\nIteration: 76  Options:  {'c1': 0.8608140875614461, 'c2': 2.02, 'w': 0.35142992193123407}\nIteration: 77  Options:  {'c1': 0.8428494040384126, 'c2': 2.04, 'w': 0.350821307133995}\nIteration: 78  Options:  {'c1': 0.8250403018670246, 'c2': 2.06, 'w': 0.3502269021415575}\nIteration: 79  Options:  {'c1': 0.8073924166953819, 'c2': 2.08, 'w': 0.3496462158707742}\nIteration: 80  Options:  {'c1': 0.7899118654710782, 'c2': 2.1, 'w': 0.3490787795752519}\nIteration: 81  Options:  {'c1': 0.7726053135965205, 'c2': 2.12, 'w': 0.3485241455914203}\nIteration: 82  Options:  {'c1': 0.7554800554745198, 'c2': 2.14, 'w': 0.3479818861680258}\nIteration: 83  Options:  {'c1': 0.7385441120054486, 'c2': 2.16, 'w': 0.34745159237265394}\nIteration: 84  Options:  {'c1': 0.7218063498096469, 'c2': 2.18, 'w': 0.3469328730694381}\nIteration: 85  Options:  {'c1': 0.7052766286755895, 'c2': 2.2, 'w': 0.3464253539626105}\nIteration: 86  Options:  {'c1': 0.6889659862428663, 'c2': 2.2199999999999998, 'w': 0.34592867670100746}\nIteration: 87  Options:  {'c1': 0.6728868726545348, 'c2': 2.24, 'w': 0.34544249803904953}\nIteration: 88  Options:  {'c1': 0.657053453585897, 'c2': 2.26, 'w': 0.34496648905008775}\nIteration: 89  Options:  {'c1': 0.6414820089421402, 'c2': 2.28, 'w': 0.3445003343883481}\nIteration: 90  Options:  {'c1': 0.6261914688960386, 'c2': 2.3, 'w': 0.3440437315960089}\nIteration: 91  Options:  {'c1': 0.6112041531021342, 'c2': 2.32, 'w': 0.34359639045222895}\nIteration: 92  Options:  {'c1': 0.5965468213847226, 'c2': 2.34, 'w': 0.34315803236119463}\nIteration: 93  Options:  {'c1': 0.5822522228837674, 'c2': 2.36, 'w': 0.34272838977648734}\nIteration: 94  Options:  {'c1': 0.5683614862434021, 'c2': 2.38, 'w': 0.3423072056592845}\nIteration: 95  Options:  {'c1': 0.5549280271653059, 'c2': 2.4, 'w': 0.3418942329680971}\nIteration: 96  Options:  {'c1': 0.5420244448704603, 'c2': 2.42, 'w': 0.3414892341779263}\nIteration: 97  Options:  {'c1': 0.529756065178477, 'c2': 2.44, 'w': 0.34109198082688047}\nIteration: 98  Options:  {'c1': 0.518292202077093, 'c2': 2.46, 'w': 0.34070225308844143}\nIteration: 99  Options:  {'c1': 0.5079621434110699, 'c2': 2.48, 'w': 0.3403198393677058}\nBest cost =  3.4261311762230905e-13\nBest position =  [0.99999942 0.99999884]\n"
     ]
    }
   ],
   "source": [
    "function = fx.rosenbrock    # optimum at [1,1]\n",
    "maxiters = 100\n",
    "start_opts = {'c1':2.5, 'c2':0.5, 'w':0.9}\n",
    "end_opts= {'c1':0.5, 'c2':2.5, 'w':0.4}     # Ref:[1]\n",
    "oh_strategy={ \"w\":'exp_decay', \"c1\":'nonlin_mod',\"c2\":'lin_variation'}\n",
    "\n",
    "cost, pos=optimize(function, maxiters, oh_strategy, start_opts, end_opts)\n",
    "\n",
    "print(\"Best cost = \", cost)\n",
    "print(\"Best position = \", pos)"
   ]
  },
  {
   "source": [
    "Changing options clearly shows better convergence. Just 100 iterations on the rosenbrock function are enough to bring the cost to very low orders of e-10 which is comparable to the ones in academia. [2]\n",
    "\n",
    "References:\n",
    "\n",
    "[1] Chih, Mingchang, et al. \"Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem.\" Applied Mathematical Modelling 38.4 (2014): 1338-1350.\n",
    "\n",
    "[2] Satyanarayana Daggubati, \"Comparison of particle swarm optimization variants\""
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